Copy–move forgery poses a significant threat to social life and has aroused much attention in recent years. Although many copy‐move forgery detection (CMFD) methods have been proposed, the most existing CMFD methods are short of adaptability in detecting images, which leads to the limitation on detection effects. To solve this problem, the paper proposes a novel keypoint‐based CMFD method: second‐keypoint matching and double adaptive filtering (SMDAF). Motivated by image matching based on keypoint, the second‐keypoint matching method is designed to match keypoints extracted from copy–move forgery images, which can be used for both the single‐CMFD and the multiple‐CMFD. Then, a double adaptive filter (DAF) based on the AdaLAM algorithm and the KANN‐DBSCAN clustering algorithm to filter wrong keypoint matches adaptively are proposed, according to the distinct distribution of keypoints in each image. Finally, the forgery regions are presented by finding their convex hulls and padding them. Compared with existing methods, extensive experiments show that the SMDAF method significantly provides more efficiency in detecting images under simulated real‐world conditions, has better robustness when facing images with different post‐treatment attacks, and is more effective in distinguishing images that look copy–move forged but are real.